I have recently become familiar with the concept of the outer and inner products on vector spaces - but why have they come to be called the "outer product" and "inner product"? What is the history behind this?
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2https://math.stackexchange.com/questions/476754/what-is-inner-about-the-inner-product – Wojowu May 03 '18 at 16:48
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3http://jeff560.tripod.com/i.html quotes: "When the German Sanskrit scholar Hermann Günther Grassman (1809-1877) developed the general algebra of hypercomplex numbers, he realized that more than one type of multiplication is possible. To two of the many possible types he gave the names inner and outer. The names seem to have been chosen because they are antonyms rather than for any intrinsic meaning." – Chappers May 03 '18 at 16:50
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Compare also with inner semidirect product and outer semidirect product of, say, groups. – Dietrich Burde May 03 '18 at 16:50
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See Hermann Günther Grassman's contribution to math. – Mauro ALLEGRANZA May 03 '18 at 17:26